CRII: RI: Efficient Structure Learning and Approximation of Networks of Causally Interacting Processes

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The study of networks is important in numerous scientific domains: neuroscience, microbiology, social science, and economics, to name a few. A major challenge in these fields is to identify causal influences in the networks. Experimentation can directly determine causal influences. However, it can be more costly and less practical than passively recording activity in the network and inferring influences from those observations. There are numerous methods that can identify correlations from observational data, though identifying causal relationships often requires expert knowledge or strong modeling assumptions. There is a need for computationally efficient and statistically robust causal inference methods to extract relevant information from network time-series data to facilitate human analysis.This research aims to significantly advance the state of the art in inferring causal influences between time-series. The research develops new and efficient algorithms to learn and approximate the structure of a recently proposed probabilistic graphical model: the directed information graph. The algorithms find optimal or near-optimal approximations of the network topology that have user-controlled sparsity levels, such as the number of edges in the graph or the amount of computation performed. The quality of approximation is measured using Kullback-Leibler divergence. The work also involves proving correctness of the algorithms and developing variations that find provably-good approximations which are robust to noisy or limited data. To achieve these goals, the project develops new bounds for directed information.